\subsection{Baym's Comment}
I talked with Baym this afternoon. It took me some time to explain all the notation and convention to him.  He suggested me to think it in the coordinator space and formulate it in Green's function.  Then considering expand the abnormal Green's function around the simple close-channel bound state solution in the two-body problem.  He mentioned that I might not be able to solve it analytically, but that is similar to Bogoliubov-de Gennes equation and I should be able to do things similarly and solve it numerically at worst.  Not sure...  The main difficulty is the really thing corresponding two-body wave function is the equal-time abnormal Green's function $F(t=0)$.  It is not clear for me how to get it.  

Maybe we can use the single pole approximation as $G_0$?  No, it is not the same thing.  The $G_0$ is for the relative coordinator of two-body wave function.  

